Under its music director Alan Gilbert, the New York Philharmonic's first residency at the Barbican showed the orchestra in fine fettle. They brought a new work with them: the UK premiere of Thomas Adès's Polaris – a commission involving the Barbican as well as the NYP and other ensembles – opened their second programme. The title refers to the North Star, whose navigational role parallels the piece's anchoring in the note A. It was another demonstration of Adès's masterly orchestral writing, shimmering in the air as it moved steadily along its vast harmonic trajectory. This was a finely realised performance, the work's intricate detail as focused as its clean-edged outline.

Joyce DiDonato's mezzo-soprano sounded clear and direct in Berlioz's Nuits d'Eté song-cycle, though Gilbert's accompaniments needed a touch more intensity. But he and his players were on suitably punchy form in Stravinsky's Symphony in Three Movements, while their account of the second suite from Ravel's Daphnis and Chloé was little short of sensational in its combination of precision and sweep.

Their final concert began with Magnus Lindberg's dense Feria – its splintered textures and conflicted harmonies suggesting something darker than the Spanish festival of its title, as did its reference to Monteverdi's Lament of Ariadne. But its complexity was sharply delineated under Gilbert's unshowy direction, which continued on into Lang Lang's performance of Bartók's Second Piano Concerto.

The star pianist was certainly on top of this demanding work technically, though in the outer movements his tone seemed too light for the extraversion of the writing and the forces pitched against him; but in the disturbed nocturne of the central slow movement his dreamy lines sounded just the right note of underlying unease. His finest moment, however, came with his encore – a rip-roaring account of the Paganini/Liszt La Campanella flaunting disarming technical wizardry.

The second half was Prokofiev's Fifth Symphony, conveyed with a crystalline surface yet real depth to the tone as well as to the music making; the NYP's own encore, a performance of Bernstein's Candide overture in which every note possessed star quality, brought Broadway to the Barbican in spades.

"InstantEncore is invaluable to our marketing mix and engagement strategy. Being a medium sized orchestra, we need a powerful mobile app that is turnkey and user-friendly. InstantEncore offers all the functionality we need and more. The other great asset: the staff is friendly, knowledgeable, and always available to help."